$$\dfrac{6}{x}+\dfrac{2}{x}-\dfrac{4}{8}x=\dfrac{-x^2+16}{2x}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6}{x}+\frac{2}{x}-\frac{4}{8}x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8}{x} - \frac{ 4 : \color{orangered}{ 4 } }{ 8 : \color{orangered}{ 4 }} \cdot x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{8}{x}-\frac{1}{2}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{8}{x}-\frac{x}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{-x^2+16}{2x}\end{aligned} $$ | |
| ① | Add $ \dfrac{6}{x} $ and $ \dfrac{2}{x} $ to get $ \dfrac{8}{x} $. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{6}{x} + \frac{2}{x} & = \frac{6}{\color{blue}{x}} + \frac{2}{\color{blue}{x}} =\frac{ 6 + 2 }{ \color{blue}{ x }} = \\[1ex] &= \frac{8}{x} \end{aligned} $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 4 } $. |
| ③ | Add $ \dfrac{6}{x} $ and $ \dfrac{2}{x} $ to get $ \dfrac{8}{x} $. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{6}{x} + \frac{2}{x} & = \frac{6}{\color{blue}{x}} + \frac{2}{\color{blue}{x}} =\frac{ 6 + 2 }{ \color{blue}{ x }} = \\[1ex] &= \frac{8}{x} \end{aligned} $$ |
| ④ | Add $ \dfrac{6}{x} $ and $ \dfrac{2}{x} $ to get $ \dfrac{8}{x} $. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{6}{x} + \frac{2}{x} & = \frac{6}{\color{blue}{x}} + \frac{2}{\color{blue}{x}} =\frac{ 6 + 2 }{ \color{blue}{ x }} = \\[1ex] &= \frac{8}{x} \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{1}{2} $ by $ x $ to get $ \dfrac{ x }{ 2 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{1}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot x }{ 2 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ x }{ 2 } \end{aligned} $$ |
| ⑥ | Subtract $ \dfrac{x}{2} $ from $ \dfrac{8}{x} $ to get $ \dfrac{ \color{purple}{ -x^2+16 } }{ 2x }$. To subtract raitonal expressions, both fractions must have the same denominator. |